Assuming you mean kJ/(kg K) and kJ/(kg C), where K stands for a unit on the Kelvin temperature scale and the C for a unit on the Celsius temperature scale, the answer is yes because the Celcius and Kelvin scale have the same unit but different zero points.
Change in temperature, of say, 10K is equal to a change of temperature of 100C. Therefore, if you you have Delta temperature in the denominator of the equation, it makes no difference in the two units you mentioned (but note it is not k but K).
However, if the equation contains temperature (but not Delta temperature) in the denominator of the equation, then the two units give different values. Normally we use K. So if temperature values are given on centigrade scale we don't use those values as given, but convert them to Kelvin scale and use those values with units kJ/kg.K.
If you quote your values in kJ/kg.0C, it will not be wrong but would be non conventional. People would be misled if they are not careful in noting the peculiar usage you adopt if you give your results in kJ/kg.0C.
Radhakrishnamurty Padyala
I am sorry, I didn't notice you were talking about entropy.
Without any doubt entropy is kJ/K. Note entropy is an extensive quantity.
The units you wrote do not correspond to entropy, but to specific entropy with units kJ/kg.K.
Both the answers given above are correct and adequately illustrative. As advised above one should always use the Kelvin units for temperature. When units are in denominator we indeed are using corresponding delta value of unit magnitude on a given scale. This fact needs to be always kept in mind.